Question
Determine whether the statements below are 'Always True', 'Sometimes True', or 'Never True'. Explain your reasoning.
(i) The product of a multiple of 6 and a multiple of 3 is a multiple of 9 .
(ii) The sum of three consecutive even numbers will be divisible by 6 .
(iii) If abcdef is a multiple of 6 , then badcef will be a multiple of 6 .
(iv) $8(7 b-3)-4(11 b+1)$ is a multiple of 12 .

Answer

self

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

"I hold some pebbles, not too many, When I group them in 3's, one stays with me. Try pairing them up - it simply won't do, A stubborn odd pebble remains in my view. Group them by 5 , yet one's still around, But grouping by seven, perfection is found. More than one hundred would be far too bold, Can you tell me the number of pebbles I hold?"
Image
Which of the following numbers are not perfect squares?
(i) 2032
(ii) 2048
(iii) 1027
(iv) 1089
Given a parallelogram ABCD Complete each statement along with the definition or property used.
Image
(i) $A D=$ _____________ $\qquad\text{ }$ (ii) $\angle D C B=$ _____________
(iii) $O C=$ _____________$\qquad$ (iv) $m \angle D A B+m \angle C D A=$ _____________
If $12^2=144$ what is
(i) $(1.2)^2$
(ii) $(0.12)^2$
(iii) $(0.012)^2$
(iv) $120^2$
A bicycle dealer has ₹ 60000 to invest, when a bicycle is available for ₹ 1000. If the price of a bicycle increases by $25 \%$, then find the number of bicycle he can purchase with the same sum?
Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube :
243
A rectangular sheet of a paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case, if the sheet measures $44 cm \times 33 cm$.
Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Without using either the number names or the numerals of the Hindu number system, give a method for adding, subtracting, multiplying and dividing two numbers or two collections of sticks.
Find the coordinates of points $P, Q, R$ and $S$ in Figure.
A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.
Image